Metamath Proof Explorer

Theorem funcnvadj

Description: The converse of the adjoint function is a function. (Contributed by NM, 25-Jan-2006) (New usage is discouraged.)

Ref Expression
Assertion funcnvadj 
|- Fun `' adjh

Proof

Step Hyp Ref Expression
1 funadj 
 |-  Fun adjh
2 cnvadj 
 |-  `' adjh = adjh
3 2 funeqi 
 |-  ( Fun `' adjh <-> Fun adjh )
4 1 3 mpbir 
 |-  Fun `' adjh